Problem: $ E = \left[\begin{array}{r}4 \\ 0 \\ 0 \\ 1\end{array}\right]$ What are the dimensions of matrix $ E$ ?
The first dimension is the number of rows in the matrix. How many rows does $ E$ have? The second dimension is the number of columns in the matrix. How many columns does $ E$ have? So, $ E$ is a 4 $\times$ 1 matrix.